Question

in the rectangular prism shown below, which lines are parallel? select all that apply.
$overleftrightarrow{pq}$ and $overleftrightarrow{os}$
$overleftrightarrow{tu}$ and $overleftrightarrow{no}$
$overleftrightarrow{os}$ and $overleftrightarrow{pt}$
$overleftrightarrow{wr}$ and $overleftrightarrow{qu}$

Explanation:

1. For \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{OS}\): In a rectangular prism, opposite edges are parallel. \(PQ\) and \(OS\) are opposite edges (they are on the same - shaped faces and do not intersect, and their direction is the same), so they are parallel.
2. For \(\overleftrightarrow{TU}\) and \(\overleftrightarrow{NO}\): \(TU\) and \(NO\) are opposite edges of the rectangular prism. They lie on parallel faces and have the same orientation, so they are parallel.
3. For \(\overleftrightarrow{OS}\) and \(\overleftrightarrow{PT}\): \(OS\) and \(PT\) are opposite edges. In the rectangular prism, these edges are parallel as they are on parallel planes and have the same direction.
4. For \(\overleftrightarrow{WR}\) and \(\overleftrightarrow{QU}\): \(WR\) and \(QU\) are opposite edges. They are part of the rectangular - faced structure of the prism and are parallel.

Answer:

\(\boldsymbol{\overleftrightarrow{PQ}}\) and \(\boldsymbol{\overleftrightarrow{OS}}\), \(\boldsymbol{\overleftrightarrow{TU}}\) and \(\boldsymbol{\overleftrightarrow{NO}}\), \(\boldsymbol{\overleftrightarrow{OS}}\) and \(\boldsymbol{\overleftrightarrow{PT}}\), \(\boldsymbol{\overleftrightarrow{WR}}\) and \(\boldsymbol{\overleftrightarrow{QU}}\)